A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles

C. Carstensen, D. Gallistl, J. Hu

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Abstract

The a posteriori error analysis of conforming finite element discretisations of the biharmonic problem for plates is well established, but nonconforming discretisations are more easy to implement in practice. The a posteriori error analysis for the Morley plate element appears very particular because two edge contributions from an integration by parts vanish simultaneously. This crucial property is lacking for popular rectangular nonconforming finite element schemes like the nonconforming rectangular Morley finite element, the incomplete biquadratic finite element, and the Adini finite element. This paper introduces a novel methodology and utilises some conforming discrete space on macro elements to prove reliability and efficiency of an explicit residual-based a posteriori error estimator. An application to the Morley triangular finite element shows the surprising result that all averaging techniques yield reliable error bounds. Numerical experiments confirm the reliability and efficiency for the established a posteriori error control on uniform and graded tensor-product meshes.
Original languageEnglish
Pages (from-to)309-335
Number of pages27
JournalNumerische Mathematik
Volume124
Issue number2
DOIs
Publication statusPublished - 2013
Externally publishedYes

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Nonconforming Finite Element Method
A Posteriori Error Estimates
Rectangle
Fourth Order
Finite Element
A Posteriori Error Analysis
Finite element method
Error analysis
Macroelements
Biharmonic Problem
Integration by parts
Nonconforming Finite Element
Averaging Technique
A Posteriori Error Estimators
Tensors
Macros
Error Control
Finite Element Discretization
Tensor Product
Error Bounds

Cite this

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A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles. / Carstensen, C.; Gallistl, D.; Hu, J.

In: Numerische Mathematik, Vol. 124, No. 2, 2013, p. 309-335.

Research output: Contribution to journalArticleAcademicpeer-review

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